A
Abs
--
absolute value of a number
Adjoint
--
adjoint matrix
Alias
--
define aliases for package names
Alias In
--
temporarily override global aliases
Aliases
--
list of global aliases
Append
--
append an object to an existing list
Ascii
--
convert between characters and ascii code
B
Bin
--
binomial coefficient
BinExp, EvalBinExp
--
binomial expansion
Block
--
group several commands into a single command
BlockMatrix
--
create a block matrix
Break
--
break out of a loop
BringIn
--
bring in objects from another ring
C
Call
--
apply a function to given arguments
Cast
--
type conversion
Catch
--
catch an error
CFApprox, CFApproximants, ContFrac
--
continued fractions
Characteristic
--
the characteristic of a ring
Ciao
--
quit CoCoA
Clear
--
clear the working memory or a ring-bound memory
Close
--
close a device
CocoaLimits
--
limits on exponents and ring characteristics
CocoaPackagePath
--
returns the path to the CoCoA packages
Coefficients
--
list of coefficients of a polynomial or vector
CoeffOfTerm
--
coefficient of a term of a polynomial or vector
Colon, :, HColon
--
ideal or module quotient
ColumnVectors
--
the list of column vectors of a matrix
Comp
--
the N-th component of a list
Comps
--
list of components of a vector
Concat, ConcatLists
--
concatenate lists or lists of lists, respectively
Cond
--
conditional expression
Contrib
--
list of contributors to CoCoA
Count
--
count the objects in a list
CurrentRing
--
the current ring
D
Dashes
--
returns string of dashes
Date
--
the date
DecimalStr
--
convert rational number to decimal string
Define
--
define a function
Defined
--
check if an expression has been defined
Deg
--
the degree of a polynomial or vector
DegLexMat, DegRevLexMat, LexMat, XelMat
--
matrices for std. term-orderings
Delete
--
delete variables from the working memory
DensePoly
--
the sum of all power-products of a given degree
Der
--
the derivative of a rational function
Describe
--
information about an expression
Destroy
--
delete rings
Det
--
the determinant of a matrix
Diff
--
returns the difference between two lists
Dim
--
the dimension of a ring or quotient object
Discriminant
--
the discriminant of a polynomial
Distrib
--
the distribution of objects in a list
Div, Mod
--
quotient and remainder for integers
DivAlg
--
division algorithm
E
E_
--
canonical vector
Elim
--
eliminate variables
EqSet
--
checks if the set of elements in two lists are equal
Equals
--
returns a string of equal signs
EquiIsoDec
--
equidimensional isoradical decomposition
Error
--
return an error message
Eval
--
substitute numbers or polynomials for indeterminates
EvalHilbertFn
--
evaluate the Hilbert function
F
Fact
--
factorial function
Factor
--
factor a polynomial
Fields
--
list the fields of a record
First
--
the first N elements of a list
FirstNonZero, FirstNonZeroPos
--
the first non-zero entry in a vector
Flatten
--
flatten a list
FloatApprox
--
approx. of rational number of the form M*10^E
FloatStr, MantissaAndExponent
--
convert rational number to a float string
For
--
loop command
Foreach
--
loop command
Format
--
convert object to formatted string
Fraction
--
returns the quotient of its arguments
Function
--
return a function
Functions
--
list the functions of a package
G
GB.Complete
--
Complete an interactive Groebner-type calculation
GB.GetBettiMatrix
--
returns the Betti matrix computed so far
GB.GetNthSyz
--
returns the part of the Nth syzygy module computed so far
GB.GetNthSyzShifts
--
shifts of the Nth syzygy module computed so far
GB.GetRes
--
returns the resolution computed so far
GB.GetResLen
--
returns the length of the resolution computed so far
GB.ResReport
--
status of an interactive resolution calculation
GB.Start_GBasis
--
start interactive Groebner basis computation
GB.Start_MinGens
--
start interactive minimal generator calculation
GB.Start_MinSyzMinGens
--
start interactive calc., min. syzs. of min. gens.
GB.Start_Res
--
start interactive resolution computation
GB.start_Syz
--
start interactive syzygy computation
GB.start_SyzMinGens
--
start interactive calc. of syzygies of min. gens.
GB.Stats
--
status of an interactive Groebner-type calculation
GB.Step, GB.Steps
--
take steps in an interactive Groebner-type calculation
GBasis
--
calculate a Groebner basis
GBM, HGBM
--
intersection of ideals for zero-dimensional schemes
GCD, LCM
--
greatest common divisor, least common multiple
GenericPoints
--
random projective points
GenRepr
--
representation in terms of generators
Gens
--
list of generators of an ideal
Get
--
read characters from a device
GetErrMesg
--
returns the message associated with an error
Gin
--
generic initial ideal
GlobalMemory
--
contents of global memory
H
H.Browse
--
browse the online help system
H.Commands
--
list commands according to type
H.Man
--
search online help system (see "?, Man")
H.OutCommands
--
print command descriptions to a file
H.OutManual
--
print the online manual to a file
H.SetMore, H.UnSetMore
--
more-device for online help
H.Syntax
--
display the syntax of a command
H.Tips
--
quick tips for using online help
H.Toc
--
display the Table Of Contents of the online manual
H.Tutorial
--
run the CoCoA tutorial
Head
--
the first element of a list
Help
--
extend online help for user-defined functions
Hilbert
--
the Hilbert function
HilbertBasis
--
Hilbert basis for a monoid
HilbertPoly
--
the Hilbert polynomial
HIntersection, HIntersectionList
--
intersection of ideals
Homogenized
--
homogenize with respect to an indeterminate
HVector
--
the h-vector of a ring or quotient object
I
Ideal
--
convert an expression into an ideal
IdealAndSeparatorsOfPoints
--
ideal and separators for affine points
IdealAndSeparatorsOfProjectivePoints
--
ideal and separators for points
IdealOfPoints
--
ideal of a set of affine points
IdealOfProjectivePoints
--
ideal of a set of projective points
Identity
--
the identity matrix
If
--
conditional statement
ILogBase
--
integer part of the logarithm
Image
--
ring homomorphism
In
--
create a list satisfying given conditions
Indet
--
individual indeterminates
IndetInd
--
the index of an indeterminate
IndetIndex
--
index of an indeterminate
IndetName
--
the name of an indeterminate
Indets
--
list of current indeterminates
Insert, Remove
--
insert or remove an object in a list
Interpolate
--
interpolating polynomial
Interreduce, Interreduced
--
interreduce a list of polynomials or vectors
Intersection, IntersectionList
--
intersect lists, ideals, or modules
Inverse
--
multiplicative inverse
IO.SprintTrunc
--
convert to a string and truncate
Iroot
--
integer part of r-th root of an integer
IsEven, IsOdd
--
test whether an integer is even or odd
IsHomog
--
test whether given polynomials are homogeneous
IsIn
--
check if one object is contained in another
IsNumber
--
checks if the argument is a number
IsPosTo, IsToPos
--
checks the module term-ordering of a ring
IsPrime
--
prime integer test
Isqrt
--
computes the (truncated) square root of an integer
IsStable, IsStronglyStable, IsLexSegment
--
checks if an ideal is stable (resp. strongly stable or a lex-segment)
IsSubset
--
checks if the elements of one list are a subset of another
IsTerm
--
checks if the argument is a term
IsZero
--
test whether an object is zero
J
Jacobian
--
the Jacobian of a list of polynomials
K
L
Last
--
the last N elements of a list
Latex
--
LaTeX formatting
LC
--
the leading coefficient of a polynomial or vector
Len
--
the length of an object
LinKer
--
find the kernel of a matrix
LinSol
--
find a solution to a linear system
List
--
convert an expression into a list
LM
--
the leading monomial of a polynomial or vector
Log
--
the list of exponents of the leading term of a polynomial
LogToTerm
--
returns a monomial (power-product) with given exponents
LPos
--
the position of the leading power-product in a vector
LPP
--
the leading power-product of a polynomial or vector
LT
--
the leading term of an object
M
MapDown
--
convert a constant polynomial to a number
Mat
--
convert an expression into a matrix
Max, Min
--
a maximum or minimum element of a sequence or list
MDeg
--
multi-degree of an polynomial
Memory
--
contents of local memory or ring-bound memory
MinGens
--
list minimal generators
Minimalize, Minimalized
--
remove redundant generators
Minors
--
list of minor determinants of a matrix
MinSyzMinGens
--
minimal generators of syzygies of minimal generators
Mod2Rat
--
reconstructing rationals from modular integers
Module
--
convert an expression into a module
Monic
--
divide polynomials by their leading coefficients
Monomials
--
the list of monomials of a polynomial or vector
MonsInIdeal
--
ideal generated by the monomials in an ideal
More
--
print a string, N lines at a time
Multiplicity
--
the multiplicity (degree) of a ring or quotient object
N
NewId
--
create a new identifier
NewList
--
create a new list
NewMat
--
create a new matrix
NewVector
--
create a new vector
NextPrime
--
find the next largest prime number
NF
--
normal form
NFsAreZero
--
test if normal forms are zero
NonZero
--
remove zeroes from a list
Not, And, Or
--
boolean operators
NR
--
normal reduction
Num, Den
--
numerator, denominator
NumComps
--
the number of components of a vector
NumIndets
--
number of indeterminates
O
OpenIFile, OpenOFile
--
open input or output file
OpenIString, OpenOString
--
open input or output string
OpenLog, CloseLog
--
open or close a log of a CoCoA session
Option
--
status of a panel option
Ord
--
matrix defining a term-ordering
P
Packages
--
list of loaded packages
Panel
--
print status of a panel's options
Panels
--
list of CoCoA panels
Partitions
--
partitions of an integer
Permutations
--
returns all permutations of the entries of a list
Pfaffian
--
the Pfaffian of a skew-symmetric matrix
PkgName
--
returns the name of a package
Poincare, HilbertSeries
--
the Poincare series
Poly
--
convert an expression into a polynomial
PrimaryDecomposition
--
primary decomposition of an ideal
Print On
--
print to an output device
Print, PrintLn
--
print the value of an expression
Product, Sum
--
the product or sum of the elements of a list
Q
Quit
--
quit CoCoA
QuotientBasis
--
vector space basis for zero-dimensional quotient rings
QZP, ZPQ
--
change field for polynomials and ideals
R
Radical
--
radical of an ideal
RadicalOfUnmixed
--
radical of an unmixed ideal
Rand
--
random integer
Randomize, Randomized
--
randomize the coefficients of a given polynomial
Rank
--
rank of a module
RealRootRefine
--
refine a root of a univariate polynomial over Q
RealRoots
--
computes a root of a univariate polynomial over Q
Record
--
create a record
ReducedGBasis
--
compute a reduced Groebner basis
Repeat
--
loop command
Res
--
free resolution
Reset
--
reset panels and random number seed to defaults
ResetPanels
--
reset panels to their default values
Resultant
--
the resultant of two polynomials
Return
--
exit from a structured command
Reverse, Reversed
--
reverse a list
Ring
--
returns the ring with a given name
RingEnv
--
name of the current ring
RingEnvs
--
names of all defined rings
RootBound
--
bound on roots of a polynomial over Q
S
Saturation, HSaturation
--
saturation of ideals
ScalarProduct
--
scalar product
Seed
--
seed for
Rand
SeparatorsOfPoints
--
separators for affine points
SeparatorsOfProjectivePoints
--
separators for projective points
Set
--
remove duplicates from a list
Set, Unset
--
set and unset panel options
Shape
--
extended list of types involved in an expression
Size
--
the amount of memory used by an object
Skip
--
does nothing
Sort, Sorted
--
sort a list
SortBy, SortedBy
--
sort a list
Source, <<
--
read commands from a file or device
Spaces
--
return a string of spaces
Sprint
--
convert to a string
StarPrint
--
print polynomial with *'s for multiplications
Starting
--
list functions starting with a given string
Submat
--
submatrix
Subsets
--
returns all sublists of a list
Subst
--
substitute values for indeterminates
Support
--
the list of terms of a polynomial or vector
Sylvester
--
the Sylvester matrix of two polynomials
Syz
--
syzygy modules
SyzMinGens
--
syzygy module for a set of minimal generators
SyzOfGens
--
syzygy module for a given set of generators
T
Tag
--
returns the tag string of an object
Tagged, Untagged, @
--
tag or untag an object for pretty printing
Tail
--
remove the first element of a list
TensorMat
--
returns the tensor product of two matrices
Toric
--
saturate toric ideals
Toric.CheckInput
--
check input to
Toric
Transposed
--
the transposition of a matrix
Tuples
--
N-tuples
Type
--
the data type of an expression
TypeOfCoeffs
--
type of the coefficients of the current ring
Types
--
lists all data types
U
Use
--
command for making a ring active
Using
--
perform commands in non-active ring
V
Var
--
function calls by reference, other complex referencing
Vector
--
create a vector
W
WeightsList
--
first row of the weights matrix
WeightsMatrix
--
matrix of generalized weights for indeterminates
While
--
loop command
WithoutNth
--
removes the N-th component from a list
WLog
--
weighted list of exponents
X
Y
Z